Question

An owner wants to receive a net amount from sale of a property of $200,000. the broker commission is 6 percent of the gross sale price. The gross price necessary (to the nearest hundred dollars) to achieve this will be ____.

1. $212,800 (212800, or 212766)
2. $212,000

Answer 1

An owner wants to receive a net amount from sale of a property of $200,000. the broker commission is 6 percent of the gross sale price. The gross price necessary (to the nearest hundred dollars) to achieve this will be $212,800.

The correct option is:

1. $212,800

Step-by-step explanation:

To calculate the gross sale price required, we can use the formula:

`\[ \text{Gross Sale Price} = \frac{\text{Net Amount}}{(1 - \text{Commission Rate})} \]`

In this case, the net amount is $200,000, and the commission rate is 6 percent (or 0.06). Substituting these values into the formula:

`\[ \text{Gross Sale Price} = (200,000)/((1 - 0.06)) \]`

`\[ \text{Gross Sale Price} = (200,000)/(0.94) \]`

`\[ \text{Gross Sale Price} \approx 212,765.96 \]`

Therefore, the gross sale price necessary to achieve a net amount of $200,000 is approximately $212,765.96. Rounding to the nearest hundred dollars, the final answer is $212,766.

In real estate transactions, the gross sale price is the total amount before any deductions, and the net amount is what the owner receives after subtracting expenses like the broker's commission. The formula adjusts for the commission by dividing the desired net amount by the complement of the commission rate. This ensures that after the commission is deducted, the owner receives the intended net amount.

In this scenario, the owner would need a gross sale price of approximately $212,766 to achieve a net amount of $200,000 after a 6 percent broker commission. It's crucial for sellers to be aware of these calculations to set realistic expectations and make informed decisions in real estate transactions.

Therefore, the correct option is : 1. $212,800